Laws of Exponents

Exponents

100

Evaluate: 3^2

9

200

Identify the base: 10x⁵

x

300

Write using exponents: (3 x 3 x 3 x 3 x 3)

3⁵

400

Write using exponents: 3 x h x h x h x h x h x h x h

3h⁷

500

Evaluate: 10(5)² - 60

190

Product of Powers

100

You do this to the exponents to multiply powers with the same base.

Add the exponents

200

Simplify: 5² x 5⁶

What is 5⁸

300

Simplify: x¹⁰ times x²

x¹²

400

Simplify: (8x³)(-3x⁹)

 -24x¹²

500

Solve for b: w³(w^b) = w^-3

b = -6

Quotient of Powers

100

You do this to the exponents when dividing powers with the same base.

Subtract the exponents

200

Simplify: 2⁵/2²

2³

300

Simplify: w³/w⁸

 w^-5

400

(18a⁷)/(6a³)

3a⁴

500

Solve for m: (12x²)/(mx³)

 2x^-1

Power of Powers

100

You do this to the exponents when finding the power to a power.

Multiply the exponents

200

Simplify: (z¹¹)⁵

 z⁵⁵

300

Simplify: (4³)²

4⁶

400

Simplify: (4y)⁴

256y⁴

500

Simplify: (2x²y⁶)³

8x⁶y¹⁸

Negative and Zero Exponents

100

Any number raised to the zero power is

 1

200

456⁰

1

300

Evaluate: 4^-2

1/16

400

Write using a positive exponent: w³/w⁸

 1/w⁵

500

Write 2x^-1 using positive exponents.

2/x¹